Given the function g(x) = x^3 − x, what is the value of g(3)?

Answer:

C. 135

Step-by-step explanation:

The value of the expression when x = 5 is 135.To find the value of the expression when x = 5, substitute the value of x into the expression and perform the calculations:

Expression: [tex](2x^2 / x) + x(100 - 15x)[/tex]

Now, replace x with 5:

[tex](2 * 5^2 / 5) + 5(100 - 15 * 5)[/tex]

Calculate the values within the parentheses first:

[tex](2 * 25 / 5) + 5(100 - 75)[/tex]

Now, perform the arithmetic inside each set of parentheses:

[tex](50 / 5) + 5(25)\\50 / 5 = 10[/tex]

Now, continue:

10 + 5 * 25 = 10 + 125 = 135

So, the value of the expression when x = 5 is 135.

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Answer:

$168,500,000

Step-by-step explanation:

Given that :

Total amount spent on both scanner and video digitizer research and development = $242,000,000

Let :

amount spent on scanner = x

Amount spent on video digitizer = y

Total amount spent, c = x + y

x = y + 95,000,000

Hence,

242000000 = y + 95,000,000 + y

242000000 - 95000000 = 2y

147,000,000 = 2y

y = $73,500,000

Hence, amount spent on scanners :

$73,500,000 + $95,000,000

= $168,500,000

Answer:

The absolute change in the height of the water is 9.5 inches

Step-by-step explanation:

Given

[tex]l =24in[/tex] --- length

[tex]w = 15in[/tex] --- width

[tex]h =12in[/tex] --- height

[tex]V_1 = 900in^3[/tex] --- the volume removed

Required

The absolute change in the height of the water

First, calculate the base area (b):

[tex]b = l * w[/tex]

[tex]b =24in * 15in[/tex]

[tex]b =360in^2[/tex]

The height of the water that was removed is:

[tex]H = \frac{V_1}{b}[/tex] i.e. the volume of the water removed divided by the base area

[tex]H = \frac{900in^3}{360in^2}[/tex]

[tex]H = \frac{900in}{360}[/tex]

[tex]H = 2.5in[/tex]

The absolute change in height is:

[tex]\triangle H = |h - H|[/tex]

[tex]\triangle H = |12in - 2.5in|[/tex]

[tex]\triangle H = |9.5in|[/tex]

[tex]\triangle H = 9.5in[/tex]

Answer:

x<4

Step-by-step explanation:

To solve for x in the inequality equation, the terms should be rearranged such that x is on one side and integers are on the other side.

First, expand 4(x-3).

This will obtain:

[tex]4x - 12 < 2x - 4[/tex]

Now, shift x terms and integers on each side.

[tex]4x - 2x < - 4 + 12[/tex]

After simplifying, it will get:

[tex]2x < 8[/tex]

Finally, we can solve for x.

[tex]x < 4[/tex]

We can also draw the respective graph (please don't mind my drawings), where the area shaded in green is the range.

Answer:

f(g(x)) = x^2+4x+3

Step-by-step explanation:

f(x) = x^2 – 1

g(x) = x + 2

f(g(x))=g(x)^2-1=(x+2)^2-1=x^2+4x+4-1=x^2+4x+3

well, first off let's notice something about angle "t", is between π and 3π/2, or namely the III Quadrant, where both "x" or adjacent side as well as "y" or opposite side are negative.

something else noteworthy is that, the hypotenuse is just a radius length and thus is never negative.

[tex]tan(t)=\cfrac{2}{3}\implies tan(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{adjacent}{-3}}\qquad \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c =\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+(-2)^2}\implies c = \sqrt{9+4}\implies c = \sqrt{13}[/tex]

[tex]\rule{34em}{0.25pt}\\\\ sec(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{adjacent}{-3}}~\hfill cos(t)=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-3\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-3\sqrt{3}}{13}[/tex]

[tex]sin(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-2\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-2\sqrt{13}}{13} \\\\\\ csc(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{opposite}{-2}}~\hfill cot=\cfrac{\stackrel{adjacent}{-3}}{\underset{opposite}{-2}}\implies \cfrac{3}{2}[/tex]

Answer: [tex]\dfrac{4}{5}\ \text{ounces}\ \text{or}\ 0.8\ \text{ounces}[/tex]

Step-by-step explanation:

Given

There is 4 fluid ounces of red paint which needs to be shared among 5 students

So, division operation is needed to deduce the ounces of red paint each student will get

Each student get

[tex]\Rightarrow \dfrac{4}{5}\ \text{ounces}\ \text{or}\ 0.8\ \text{ounces}[/tex]

Answer:

Let x be one of the numbers

then since they differ by 3... Let (x-3) be the 2nd Number

Their product is 88

(x-3)x = 88

x²-3x =88

x² - 3x - 88=0

Solving The quadratic eqn

x=11 or x = -8.

To check this answer

since the Numbers are x and x-3

x= 11

x-3 = 11 - 3 = 8

(x-3)x = 8x11 = 88.

Or When x=-8

(x-3) = -8 - 3 = -11

x= -8

(x-3)x = -8 x - 11 = 88.

Have a great day!

Answer:

First Set: [11, 8], Second Set: [-8, -11]

Step-by-step explanation:

The first number will be x. The second number is x-3. So now make an equation: x(x-3)=88 because their product equals 88. So now solve.

Solving:

[tex](x)(x-3)=88[/tex]

[tex]x^{2}-3x-88=0[/tex]

Now you can factor:

[tex](x-11)(x+8)=0[/tex]

[tex]x=11, x=-8[/tex]

Now plug in each number for x for the following equation:

[tex](x)(x-3)=88[/tex]

[tex](11)(11-3)=88[/tex]

[tex]88=88[/tex]

This is true.

[tex](-8)(-8-3)=88[/tex]

[tex]88=88[/tex]

This is true.

Both are true. So now you have two sets of answers.

Your welcome!

Answer:

0.76

or

-0.76

hope this helps

Complete question is;

Which set of numbers is included as part of the solution set of the compound inequality

x < 6 or x > 10?

A) {–7, –1.7, 6.1, 10}

B) {–3, 4.5, 13.6, 19}

C) {0, 6, 9.8, 14}

D) {8.5, 9.1}

Answer:

B) {–3, 4.5, 13.6, 19}

Step-by-step explanation:

The given compound inequality x < 6 or x > 10 means that x must be less than 6 and greater than 10. And also that x cannot fall between 6 and 10.

Looking at the given options, the only set of values that fall into this compound inequality range is option B.

Answer:

Step-by-step explanation:

angle 1 and angle 2 add to 180 degree because they are supplementary angel and in supplementary angle sum of two angles is 180 degree

angle 1 and angle 3 is equal as they are vetically opposite angles and vertically opposite angles are always equal.

angle 3 and 4 add to 180 degree because they are supplementary angle and in supplementary angle sum of two angles id 180 degree.

angle 2 and angle 4 are equal because they are vertically opposite angles and vertically opposite angles are always equal.

Answer:

[tex]p > s[/tex]

Step-by-step explanation:

Given

[tex]p \to poncho[/tex]

[tex]s \to scarf[/tex]

Required

The inequality

From the question, we understand that;

the number of p used is more than the number of s

more than means greater than.

So, the inequality is:

[tex]p > s[/tex]

To represent this on a number line.

First, we identify the position of s (i.e. scarf)

[tex]p > s[/tex] implies that p is any point to the right of s

Answer: 100 = 10d + 5

Step-by-step explanation:

Dolls are sold for $10 each so when checking the total amount made from the sale of d dolls you will multiply d by the price of each doll:

= 10 * d

= 10d

There is a $5 charge for shipping but this is one time so it is added to the total price of d dolls:

= 10d + 5

The total made was $100 so the equation above should equal $100:

100 = 10d + 5

Answer:

a)  (10×13) + 55 b) 185 Nu c)-75 or -205 (unsure of instruction)

Step-by-step explanation:

a) He spends 10 Nu a day for 13 days, meaning he has spent 10×13 Nu. He originally had this amount, plus the 55 he ends up with. This means he began with (10×13) + 55.

b) This can then be solved using BODMAS (or PEMDAS, whatever you call the order of operations).

We begin with the multiplication, which turns the expression to 130+55. We then move to addition, giving a final result of 185.

c) For this one, I'm not sure if it is if he did that from the beginning or from now, so I've done both.

If it's from the beginning, you would use 185-(20×13) to solve this. This gives 185-260, which solves to -75.

If it's from the point of 55 Nu, you would use 55-(20×13), which gives 55-260. This solves to -205.

**You may wish to revise writing integer expressions. I'm always happy to help!

Answer:

A) A = 275 + 125x

B) 1850 - 100x

C) 7 months

D) 13 months

Step-by-step explanation:

He has $275 saved.

He plans to save $125 each month.

We are told that the computer is currently $1,850

And the price drops $100 each month.

Thus;

A) If x represents the number of months, then equation of the amount he will save is;

A = 275 + 125x

B) If x represents the number of months, then equation to represent the total cost is;

1850 - 100x

C) To find the Number of months he will need to save, we will equate gotten in question A to the equation gotten in question B. Thus;

275 + 125x = 1850 - 100x

Rearranging;

125x + 100x = 1850 - 275

225x = 1575

x = 1575/225

x = 7 months

D) If the price doesn't drop like he is anticipating, then the cost will still be $1850. Thus;

275 + 125x = 1850

125x = 1850 - 275

125x = 1575

x = 1575/125

x = 12.6 months

Approximating to the nearest whole number gives 13 months

Answer:

Step-by-step explanation:

20 houses

Answer:

20

Step-by-step explanation:

You would set it up as 8:5=32:x. Since you are multiplying the number of cars by 4, you should do the same with houses. This gives 32:20, meaning there are 20 houses on the block.

**You may want to revise multiplying and dividing with ratios. I'm always happy to help!

Answer:

3n - 3

Step-by-step explanation:

Answer:

3n-3

Step-by-step explanation:

n-1(1-n)-1 = n- 1 + n - 1 = 2n-2

1 - (2n-2) = 1 - 2n + 2

n - (1 - 2n + 2) = n - 1 + 2n -2 which equals 3n - 3

Answer: B.

Step-by-step explanation:

Data: Estimate of 7.21x3.86/10.09=x

Only step, Find the estimate for each number(7.21=7, 3.86=4, 10.09=10)

Explanation: How estimation work is that it numbers below 5 stays the same and numbers 5 and above round up so a number like 7.21 which has 2 and 1 as it's rounding numbers will stay the same however a number like 3.86 which has 8 and 6 as it's rounding numbers will round up

That's how we arrive at the answer of B.

I hope this helps(Mark brainliest if you'd like)

Answer:

x = 3 1/2

Step-by-step explanation:

8/14 = 2/x

Using cross products

8*x = 14*2

8x = 28

Divide by 8

8x/8 = 28/8

x = 7/2

x = 3 1/2

Step-by-step explanation:

Decide on the number of classes.

Determine the range, i.e., the difference between the highest and lowest observations in the data.

Divide range by the number of classes to estimate approximate size of the interval

hope it helps.

Answer:

104.6

just use the cone formula and add the two together.

Answer:

a) 9:11 am

b) 77°F

Step-by-step explanation:

a) From the clock shown in the image attached, we can see that the time that the sprinkler system is switched off is at 11:56 am. Since the strawberries are watered for a total of 2 hours and 45 minutes every day, the time that the sprinkler is switched on can be gotten by subtracting 2 hours 45 minutes from 11:56 am. Hence:

Time sprinkler system is switched on = 11:56 am - 2 hours 45 minutes = 9:11 am

b) Temperature in °Farenheit = (1.8 * temperature in degree Celsius) + 32°

Temperature in °Farenheit = (1.8 * 25°) + 32° = 45° + 32°

Temperature in °Farenheit = 77°F

Answer:

opposite of each other

Hope this helps!

Answer:

3x^2

Step-by-step explanation:

The length of the leg is 9.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

From the triangle,

S = length of the leg.

Now,

Applying the Pythagorean theorem.

√18² = 3² + s²

18 = 9 + s²

s² = 18 - 9

s² = 9

s = 9

Thus,

The length of the leg is 9.

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Answer:

True

Step-by-step explanation:

This is an Isosceles triangle because it has two equal sides.

Answer:

19.0 in

Step-by-step explanation:

From the question given above, the following data were:

Volume (V) of sphere = 28526 in³

Pi (π) = 3.14

Radius (r) =?

The radius of the sphere can be obtained as follow:

V = 4/3 πr³

28526 = 4/3 × 3.14 r³

28526 = 12.56r³ / 3

Cross multiply

12.56r³ = 28526 × 3

12.56r³ = 85578

Divide both side by 12.56

r³ = 85578 / 12.56

Take the cube root of both side

r = ³√(85578 / 12.56)

r = 19.0 in

Thus, the radius of the sphere is 19.0 in

Answer:

1) 187.5ms^2

1) 187.5ms^22) 307.5m

Step-by-step explanation:

1) You can use the formula:

Force = Mass x Acceleration

750 = 4 x a

750 = 4a

750/4 = a

187.5ms^2

2)

For every one second it travels 12.3 meters therefore you can just do 12.3x25 = 307.5m